Empirical evidence can never establish mathematical existence--nor can the mathematician's demand for existence be dismissed by the physicist as useless rigor. Only a mathematical existence proof can ensure that the mathematical description of a physical phenomenon is meaningful.
Richard CourantRelated topics
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Indeed, proof that a given condition always precedes or accompanies a phenomenon does not warrant concluding with certainty that a given condition is the immediate cause of that phenomenon. It must still be established that when this condition is removed, the phenomen will no longer appear.
Claude Bernard
Poverty is a bitter thing; but it is not as bitter as the existence of restless vacuity and physical, moral, and intellectual flabbiness, to which those doom themselves who elect to spend all their years in that vainest of all vain pursuits-the pursuit of mere pleasure as a sufficient end in itself.
Theodore Roosevelt